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Select this link to open drop down to add material 18.152 Introduction to Partial Differential Equations (MIT) to your Bookmark Collection or Course ePortfolio

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This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for...
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This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for elliptic; hyperbolic and parabolic differential operators; method of characteristics; review of Lebesgue integration; distributions; fourier transform; homogeneous distributions; asymptotic methods.

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Select this link to open drop down to add material 18.155 Differential Analysis to your Bookmark Collection or Course ePortfolio

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The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear...
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The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear partial differential equations.Ã‚Â It is the second semester of a two-semester, graduate-level sequence on Differential Analysis.

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Select this link to open drop down to add material 18.156 Differential Analysis to your Bookmark Collection or Course ePortfolio

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Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field...
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Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.

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This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave...
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This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods and tools for solving these PDEs, such as separation of variables, Fourier series and transforms, eigenvalue problems, and Green's functions.

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Select this link to open drop down to add material 18.303 Linear Partial Differential Equations to your Bookmark Collection or Course ePortfolio

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This course provides students with the basic analytical and computational tools of linear partial differential equations...
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This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems.

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This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction...
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This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.

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Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied...
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Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own.

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The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate...
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The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.

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This course emphasizes concepts and techniques for solving integral equations from an applied mathematics perspective....
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This course emphasizes concepts and techniques for solving integral equations from an applied mathematics perspective. Material is selected from the following topics: Volterra and Fredholm equations, Fredholm theory, the Hilbert-Schmidt theorem; Wiener-Hopf Method; Wiener-Hopf Method and partial differential equations; the Hilbert Problem and singular integral equations of Cauchy type; inverse scattering transform; and group theory. Examples are taken from fluid and solid mechanics, acoustics, quantum mechanics, and other applications.

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